lecture20-annotated - Machine Learning 10-701/15-781, Fall...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Eric Xing © Eric Xing @ CMU, 2006-2008 1 Machine Learning Machine Learning 10 10 -701/15 701/15 -781, Fall 2008 781, Fall 2008 Learning Graphical Models Learning Graphical Models Eric Xing Eric Xing Lecture 20, November 19, 2008 Reading: Chap. 8, C.B book X1 X2 X3 X4 X5 X6 X7 X8 Visit to Asia Tuberculosis Tuberculosis or Cancer XRay Result Dyspnea Bronchitis Lung Cancer Smoking Eric Xing © Eric Xing @ CMU, 2006-2008 2 BN and Graphical Models z A Bayesian network is a special case of Graphical Models z A Graphical Model refers to a family of distributions on a set of random variables that are compatible with all the probabilistic independence propositions encoded by a graph that connects these variables z It is a smart way to write / specify / compose / design exponentially-large probability distributions without paying an exponential cost, and at the same time endow the distributions with structured semantics A C F G H E D B ) ( 8 7 6 5 4 3 2 1 ,X ,X ,X ,X ,X ,X ,X X P ) , ( ) ( ) , ( ) | ( ) | ( ) | ( ) ( ) ( ) ( : 6 5 8 6 7 4 3 6 2 5 2 4 2 1 3 2 1 8 1 X X X P X X P X X X P X X P X X P X X X P X P X P X P =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Eric Xing © Eric Xing @ CMU, 2006-2008 3 z Directed edges give causality relationships ( Bayesian Network or Directed Graphical Model ): z Undirected edges simply give correlations between variables ( Markov Random Field or Undirected Graphical model ): Two types of GMs X1 X2 X3 X4 X5 X6 X7 X8 Receptor A Kinase C TF F Gene G Gene H Kinase E Kinase D Receptor B X1 X2 X3 X4 X5 X6 X7 X8 Receptor A Kinase C TF F Gene G Gene H Kinase E Kinase D Receptor B P ( X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 ) = P ( X 1 ) P ( X 2 ) P ( X 3 | X 1 ) P ( X 4 | X 2 ) P ( X 5 | X 2 ) P ( X 6 | X 3 , X 4 ) P ( X 7 | X 6 ) P ( X 8 | X 5 , X 6 ) P ( X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 ) = 1/Z exp{ E ( X 1 ) +E ( X 2 ) +E ( X 3 , X 1 )+ E ( X 4 , X 2 ) +E ( X 5 , X 2 ) + E ( X 6 , X 3 , X 4 )+ E ( X 7 , X 6 )+ E ( X 8 , X 5 , X 6 )} Eric Xing © Eric Xing @ CMU, 2006-2008 4 Structure: DAG • Meaning: a node is conditionally independent of every other node in the network outside its Markov blanket • Local conditional distributions ( CPD ) and the DAG completely determine the joint dist. •G i ve causality relationships, and facilitate a generative process X Y 1 2 Descendent Ancestor Parent Children's co-parent Child Bayesian Network: Conditional Independence Semantics
Background image of page 2
3 Eric Xing © Eric Xing @ CMU, 2006-2008 5 Undirected graphical models z Pairwise (non-causal) relationships z Can write down model, and score specific configurations of the graph, but no explicit way to generate samples z Contingency constrains on node configurations X 1 4 2 3 5 Eric Xing © Eric Xing @ CMU, 2006-2008 6 Canonical examples z The grid model z Naturally arises in image processing, lattice physics, etc. z Each node may represent a single "pixel", or an atom z The states of adjacent or nearby nodes are "coupled" due to pattern continuity or electro- magnetic force, etc.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/26/2010 for the course MACHINE LE 10701 taught by Professor Ericp.xing during the Fall '08 term at Carnegie Mellon.

Page1 / 17

lecture20-annotated - Machine Learning 10-701/15-781, Fall...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online